TableofContents
TableofContents
IntroductoryPhysicsV1
Introduction
Lab1:യTheScientificMethod
Lab2:യLabReports
Lab3:Measurements
NewtonianMechanics
Lab4:യTypesofForce
Lab5:Newton’sLaws
Lab6:യLinearMotion
Lab7:യProjectileMotion
Lab8:യCircularMotion
Lab9:യCenterofMass
Lab10:യGravity
Lab11:യEnergy
Lab12:യMomentum
Lab13:യMechanicalAdvantage
Matter
Lab14:യExploringMatter
Lab15:യPropertiesofSolids
Lab16:യPropertiesofFluids
3
Lab7:ProjectileMotion
Lab7:ProjectileMotion
Conceptstoexplore:
x
Scalersvs.vectors
x Projectiles
x Parabolictrajectory
Figure1:Theverticalandhorizontalforcesrequiredtopullagliderintoflightcanbeachievedwithonetow
rope.
Asyoulearnedpreviously,aquantitythatconveysinformationaboutmagnitudeonly
iscalledascalar.However,whenaquantity,suchasvelocity,conveysinformation
aboutmagnitudeanddirection,wecallitavector.Alongwithcarryingthatextrabitof
informationaboutthepathofmotion,vectorsarealsousefulinphysicsbecausethey
canbeseparatedintocomponents.Infact,anyvectorcanberesolved(brokendown)
intoanequivalentsetofhorizontal(xͲdirection)andvertical(yͲdirection)components,
whichareatrightanglestoeachother.
Aprojectileisanobjectactedonbygravityalone.Typically,aprojectileisanyobject
which,onceprojected,continuesinmotionbyitsowninertiaandisinfluencedonlyby
thedownwardforceofgravity.RememberthatNewton’sLawsdictatethatforces
causeacceleration,notsimplymotion.Therefore,theonlyforceactingonaprojectile
initsFreeBodyDiagramistheforceofgravitydownward.ThismayseemcounterͲ
Figure2:Some
intuitivesincetheobjectmightinitiallybemovinginseveraldirections,bothhorizonͲ examplesofproͲ
jectilesareacanͲ
tallyandvertically,butgravityactsonlyontheverticalmotionoftheobject.
nonballfired
fromacannon,a
baseballhitbya
bat,andballs
beingjuggled.
79
Lab7:ProjectileMotion
Figure3:Noticehowthehorizontaldistancetheprojectilecoversisconstantregardlessofitsverticalmotion.
Thisshowsthataprojectile’shorizontalvelocityisconstant.Ifyoufireaprojectilehorizontallyatthesame
timeasdroppingonestraightdown,theywillhitthegroundatthesametime!Evenextremelyfastprojectiles
suchasbulletsfallattheratedeterminedbygravity.
80
Lab7:ProjectileMotion
OneconvenientthingaboutusingvectorstodescribeproͲ
jectilemotionisthatwecanseparatethevelocityofthe
projectileintohorizontalandverticalmotion.Thevertical
componentofthevelocitychangeswithtimeduetogravͲ
ity,butthehorizontalcomponentremainsconstantbeͲ
causenohorizontalforceisactingontheobject(airresisͲ
tanceaddsquiteabitofcomplicationathighervelocities
butwillbeneglectedinthislab).Sinceprojectilesmovein
twodimensions(verticalandhorizontal),thisallowsfor
independentanalysisofeachcomponentoftheobject’s
motion.Thecombinationofa(constantly)changingvertical
velocityandaconstanthorizontalvelocitygivesaprojecͲ
tile’strajectorytheshapeofaparabola.
AsshowninFigure3,theprojectilewithhorizontalandverͲ
ticalmotionassumesacharacteristicparabolictrajectory
duetotheeffectsofgravityontheverticalcomponentof
motion.ThehorizontalmotionistheresultofNewton’s
FirstLawinaction–theobject’sinertia!Ifairresistanceis
neglected,therearenohorizontalforcesactinguponproͲ
jectile,andthusnohorizontalacceleration.Itmightseem
surprising,butaprojectilemovesatthesamehorizontal
Figure4:Whenaprojectile(water,inthis
speednomatterhowlongitfalls!
case)islaunchedupward,theverticalaccelͲ
erationwillreachzeroatthetopofthepaͲ rabola.Asgravitypullstheobjecttowardthe Thekinematicsfromthepreviouslabcandescribeboth
Earth,theobjectaccelerates.HorizontalveͲ componentsofthevelocityseparately.FormosttwoͲ
locityremainsconstantthroughout
dimensionalprojectilemotionproblems,thefollowing
thismotion.
fourequationswillallowyoutosolvefordifferentaspects
ofaprojectile’sflight,aslongasyouknowtheinitialposiͲ
tionandtheinitialvelocity.Thetwonewequationscanbe
obtainedthroughsubstitution.
Figure5:FourusefulkinematicequaͲ InthislabyoucanassumethatprojectilesarefiredeithervertiͲ
tionsforprojectilemotion:
callyorhorizontally,sothattheinitialvelocitiesineithercase
willbeeither:
vo=vyo
or
vo=vxo.
Usingtheequationsabove,youcancalculatethetotaldistance
orrange,R,ofaprojectile.Iftheprojectileisfiredatanangle,
therangeisafunctionoftheinitialangleɽ,theinitialvelocity
andtheforceofgravity.Usingalittlealgebra,youcanderivethis
expressionusingthekinematicsequationsabove:
81
Lab7:ProjectileMotion
Figure6:Thepathofaprojectileintheabsenceofairresistanceisaperfectparabola(top);withairresistance
thetrajectorylookslikea“squashed”യparabola,andtherangeoftheobject’sflightisnoticeablyaffected.
R=v2sin(2ɽ)
g
Itisimportanttorememberthatinmanycases,airresistanceisnotnegligibleandaffectsboththe
horizontalandverticalcomponentsofvelocity.Whentheeffectofairresistanceissignificant,the
rangeoftheprojectileisreducedandthepaththeprojectilefollowsisnotatrueparabola.
82
Lab7:ProjectileMotion
Experiment1:Calculatingthedistancetraveledbyaprojectile
Theobjectiveofthislabistopredicttherangeofaprojectilesetinmotion.
Materials
Ramp
Marble
Cornstarch
4sheetsofblackconstructionpaper
Tapemeasure
Monofilamentline
Fishingsinker
Procedure1
1. Placetheramponatableandmarkthelocationatwhichyou
willreleasethemarble.Thiswillensurethemarbleachieves
thesamevelocitywitheachtrial.
2. Createaplumblinebyattachingthefishingsinkertothe
Figure7:യRampsetupdiagram
monofilamentline.
3. Holdthestringtotheedgeoftheramp,andmarkthespotat
whichtheweighttouchestheground.Note:Theplumblinehelpstomeasuretheexactdistance
fromtheedgeoftheramptothepositionwherethemarble“lands.”
4. Laydownarunwayofconstructionpaper.
5. Wetthemarblealloverwithwater,anddropintothecornstarchbagtocoat.Rollonapapertowel
toachieveasmooth,evencoatofcornstarchalloverthemarble(youdonotwantanychunksasit
willaffectthepathofmotion.)Whenthemarblehitstheconstructionpaper,theforcewillcause
someofthecornstarchtocomeoff,andleaveamarkontheconstructionpapersoyoucansee
thepointoffirstcontact!
6. Begintheexperimentbyreleasingthemarbleatthemarkedpointontheramp.
7. Measurethedistancetraveledtothefirstmarkmadeonthecarbonpaperusingthetapemeasure.
RecordthisvalueinTable1onthefollowingpage.
8. Repeatsteps5Ͳ7ninemoretimesandrecordyourdatainTable1.
9. Next,useyourdatatocalculatethevelocityofthemarbleforeachtrial.
Procedure2
1. Findahighertable,orstacksomebooksunderneaththeramptoincreasetheheight.Measurethe
startingheightattheendoftherampasbefore.
2. Usingtheaveragevelocityfoundearlier,predicthowfarawaythemarblewilllandusingthekineͲ
maticequations.RecordthisdistanceinTable2.(Hint:youcaneitheruseoneequationtofindthe
totaltimeintheairusingtheinitialandfinalheights,andanothertofindthehorizontaldistance,
oryoucanusetherangeequationwithɽ=0.)
3. Measurethisdistanceoutandmarkitbeforeyoureleasethemarble.Releasethemarblefour
timesandrecordthedistancetraveledinTable2.
83
Lab7:ProjectileMotion
Table1:Rangeandvelocityofprojectile,Procedure1
TableHeight(m) DistanceTraveled AvgDistance
AverageVelocity
Table2:Rangeofprojectile,Procedure2
TableHeight(m) ObservedDistance PredictedDistance ObservedD(avg)
Calculations:
84
Lab7:ProjectileMotion
Questions
1. Ifyouweretothrowaballhorizontallyandatthesametimedropanexactcopyoftheballyou
threw,whichballwouldhitthegroundfirstandwhyisthisso?
2. Supposeyoualteredyourexistingrampsothatthemarbleshadtwicetheirinitialvelocityright
beforeleavingtheramp.Howwouldthischangethetotaldistancetraveledandthetimethatthe
marbleswereintheair?
3. DrawaFBDforthemarblesbeforeandafteritleavestheramp.
4. Describetheaccelerationofthemarblesafteritleavestheramp.
5. DidyourpredictioninProcedure2comeclosetotheactualspot?Findthepercenterrorofyour
predicteddistance(expected)comparedtotheactualaveragedistance(observed).Whataresome
sourcesoferrorinthisexperiment?
%error=observedvalueͲexpectedvalueX100
expectedvalue
85
Lab7:ProjectileMotion
Experiment2:SqueezeRocketprojectiles
Theobjectiveofthislabistoobservethedistanceaprojectilewilltravelwhenthelaunchangleis
changed.
Materials
4SqueezeRockets™
1SqueezeRocket™Bulb
Protractor
Tapemeasure
Stopwatch
NOTE:Pleaseexercisegreatcautionwhenfiringtheserockets.Besurethelineof
fireisclearofpeopleandbreakableobjectspriortolaunchinganyrocket.
Rocketswilloftentakeunpredictableflightpaths.Toensuredataprecision,only
recordtrialsinwhichtherockettravelsaparabolicpathandcontactstheground
withthefrontendfirst.
Procedure
1.
2.
3.
4.
5.
6.
7.
8.
86
Markthespotfromwhichtherocketswillbelaunched.
LoadaSqueezeRocket™ontothebulb.
Usingaprotractor,aligntherockettoanangleof90°(vertical).
Squeezethebulb(youwillneedtoreplicatethesamepressureforeachtrial),andsimultaneously
startthestopwatchuponlaunch(alternatively,haveapartnerhelpyoukeeptime).Measureand
recordthetotaltimetherocketisintheair.Repeatthisstepthreeormoretimes,andaverage
yourresults.RecordyourresultsinTable3.
tavg=______________
Calculatetheinitialvelocityoftherocket(vinitial=voy)usingthekinematicsequations.
RecordyourcalculationinTable3.(Hint:youcantaketheinitialheightaszero.TheverticalvelocͲ
ityiszeroatthepeakoftheflight,whenthetimeisequaltot/2.)
Repeatthistrialtwomoretimes,andrecordthevaluesinTable3.
Choosefouradditionalanglestofiretherocketfrom.Beforelaunchingtherocket,calculatethe
expectedrangeusingtheverticalvelocityandtheanglefromwhichtherocketswillbefired.ReͲ
memberthatyoucanusezeroforanyinitialpositions,andthattheaccelerationduetogravity,g,
Lab7:ProjectileMotion
isͲ9.8m/s2.RecordthesevaluesinTable3.
9. Next,aligntherocketwiththefirstanglechoiceandfireitwiththesameforceyouusedinitially.
Trytorecordlauncheswheretherockettravelsinaparabolaanddoesnotstallorflutteratthe
top.Measurethedistancetraveledwiththetapemeasure.Repeatthisfortwoadditionaltrials,
recordingtheactualrangeinTable3.
10. RepeatStep7foratleast5additionalanglesandrecordthedatainTable3.
11. Recordthepercenterrorbetweenyourcalculatedandactualvaluesinthelastcolumn.
Table3:യProjectiledataforExperiment2
InitialVelocity Initial
(m/s)
Angle
90°
Predicted
Range(m)
ActualRange(m)
Average
%Error
0
*Note:%error=observedvalueͲexpectedvaluex100
expectedvalue
Questions
1. Whatistheanglethatgivesthegreatestrange?Theleast?Basedonyourresults,whichangle
shouldgivethegreatestrangeforprojectilemotion?
87
Lab7:ProjectileMotion
2. DrawaFBDforarocketlaunchedatanarbitraryangle(assumetherockethasjustonlybarelyleft
thelaunchtube,andneglectairresistance).
3. Whatroledoesairresistanceplayinaffectingyourdata?
4. Discussanyadditionalsourcesoferror,andsuggesthowtheseerrorsmightbereducedifyouwere
toredesigntheexperiment.
5. Howwouldakickeronafootballteamusehisknowledgeofphysicstobetterhisgame?Listsome
otherexamplesinsportsorotherapplicationswherethisinformationwouldbeimportantoruseͲ
ful.
88
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